Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of #4451 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×#4451 |
| Fitting | C32×#95 ⋊ C2 |
| Sylow | C32 ⋊ #327 |
218 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
117 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×#327, C2×C3×#4451, D3×#4451, … |
| maximal normal subgroup of | C3×D3×#327, C2×C3×#4451, D3×#4451, … |
| maximal quotient of | C3×#67479, C3×#67478, C3×#67612, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1077);